Control strategies for meeting time and capacity constraints in manufacturing plants based on discrete event systems

This paper addresses the control problem related to marking and strict timing constraints in Timed Event Graphs (TEGs). An analytic approach is developed to design state feedback control laws using Min-Plus formalism. In this approach, the dynamic behavior of TEGs and the mixed constraints are represented by linear equations and inequalities within the Min-Plus algebra dioid. Utilizing these mathematical frameworks, control laws are formulated to enforce the required constraints on TEG paths, provided certain sufficient conditions are met. The proposed controllers are implemented through a set of monitor places that oversee the initial TEGs, ensuring all mixed constraints are satisfied. Finally, a manufacturing system case study is presented to demonstrate the theoretical results and validate the effectiveness of the proposed methods.